Basic Derivative Information and Power Rule
Normal/Tangent Lines
Product Rule
Quotient Rule
Trig Derivatives
100
The derivative calculates the ________.
Slope
100

The slope of the tangent line of f(x).

What is f′(x)?

100
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
100
Define the Quotient Rule using f(x)/g(x)
[g(x)f′(x) - f(x)g′(x)]/ (g(x))²
100
d/dx cosx=
-sinx
200
d/dx 5 =
0
200

The slope of the normal line of f(x).

What is -1/f'(x)?

200
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
200
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
200
Differentiate y=tan(x)
y′ =sec²(x)
300
d/dx x² =
2x
300

The equation, in point-slope form, of the line tangent to y=x4 -x3 +2 at the point (2, -6).

What is y+6=20(x-2)?

300
Differentiate y=x³lnx
y′ =x²(1+3lnx)
300
Differentiate y= (1+lnx) / (x²-lnx)
y′= [(1/x)-x-2xlnx] / (x²-lnx)²
300
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
400
d/dx 3x²-x+3 =
6x-1
400

The equation, in point-slope form, of the line tangent to y=x / x-1 at the point (3, 1.5).

What is y-1.5= -1/4 (x-3)?

400
Differentiate y=e^-x²cos2x
y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x
400
f(x)= (x²-1)³/ x²+1, what is f′(x)?
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
400
d/dx sin(2x)
2cos(2x)
500
Speed is _________.
the absolute value of velocity
500

The equation, in point-slope form, of the normal line for y=x / x-1 at the point (3, 1.5).

What is y-1.5=4 (x-3)?

500
Differentiate y=x²sin³(5x)
y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]
500
Differentiate y= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
500
d/dx arcsec(x)=
1/ |x| √(x² - 1)
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